Time Resolved Investigation of the Spin Dynamics in Laterally Confined Microstrips and Heterostructures / submitted by Santa Pile

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Submitted by Santa Pile

Submitted at

Institute of Semicon-ductor and Solid State Physics Supervisor and First Evaluator Univ.-Prof. Dr. Andreas Ney Second Evaluator Univ.-Prof. Dr. Andrii Chumak March 2021 JOHANNES KEPLER UNIVERSITY LINZ Altenbergerstraße 69 4040 Linz, ¨Osterreich www.jku.at DVR 0093696

Time Resolved

Investi-gation of the Spin

Dy-namics in Laterally

Con-fined

Microstrips

and

Heterostructures

Doctoral Thesis

to obtain the academic degree of

Doktorin der Naturwissenschaften

in the Doctoral Program

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Statutory Declaration

I hereby declare that the thesis submitted is my own unaided work, that I have not used other than the sources indicated, and that all direct and indirect sources are acknowledged as references.

This printed thesis is identical with the electronic version submitted.

Santa Pile

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Abstract

The quasi-uniform ferromagnetic resonance (FMR) modes and spin-wave dynamics in a single rectangular Ni80Fe20 (permalloy, Py) microstrip (1× 5 × 0.03 µm3) under

uniform microwave field excitation are investigated by means of micromagnetic simu-lations, microresonator-/microantenna-based FMR measurements and direct imaging using time-resolved scanning transmission X-ray microscopy, combined with a ferro-magnetic resonance excitation scheme (STXM-FMR). Both measuring techniques share the same FMR excitation scheme. The direct imaging of spin waves is performed with ultimate time and space resolution and is corroborated by time-resolved micromag-netic simulations. Measurements and micromagmicromag-netic simulations show that spin waves, which are excited in a confined Py rectangular microstrip, surprisingly exhibit a non-standing character both at resonance and off resonance fields under uniform microwave excitation.

A nonstanding character of spin-waves in more complex Py microstructures is ob-served by direct imaging along with an evidence of the possibility to alter the spin-wave behavior by modifications of the sample design (arrangement of the rectangular microstrips). Microstructures consisting of two identical Py rectangular microstrips perpendicular to each other are studied using a similar approach as for the single strip samples. Using micromagnetic simulations the presence of the spin-wave modes along with the quasi-uniform FMR modes of the Py strips are calculated and confirmed by microresonator-based FMR measurements. The spin-waves are imaged in real space using STXM-FMR, which reveals a nonstanding character of the spin waves similar to the single strip sample. In addition, it is shown by micromagnetic simulations and confirmed by STXM-FMR that the spin-wave behavior can be influenced by the local magnetic stray fields, which are controlled by different mutual microstrips position. Due to its elemental selectivity STXM-FMR can also be used to directly image spin pumping in a ferromagnet-nonferromagnet heterostructure. STXM-FMR allows to di-rectly probe the spatial extent of the ac spin polarization in Co-doped ZnO (Co:ZnO) film, which is generated by spin pumping from an adjacent Py microstrip. The relative phases of the dynamic magnetization component of the two constituents are compared and they are found to be close to antiphase. The correlation between the distributions of the magnetic excitation in the Py strip and the Co:ZnO film reveals that laterally there is no one-to-one correlation. The observed distribution is rather complex, but integrating over larger areas demonstrates that the spin polarization in the nonferro-magnet extends laterally beyond the region of the ferrononferro-magnetic microstrip. Therefore, the observations are better explained by a local spin pumping efficiency and a lateral propagation of the ac spin polarization in the nonferromagnet over the range of a few micrometers.

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Zusammenfassung

Die quasi-uniformen ferromagnetischen Resonanzmoden (FMR) und die Spin-Wellen-Dynamik in einer einzelnen rechteckigen Ni80Fe20 (Permalloy, Py) Mikrostreifen (1×

5_{× 0, 03 µm}3_{) unter gleichm¨}_{aßiger Mikrowellenfeldanregung werden mittels}

mikromag-netischer Simulationen, FMR-Messungen auf Basis von Mikroresonatoren und direk-ter Abbildung mittels zeitaufgelöster Rastertransmissions-Röntgenmikroskopie, kom-biniert mit einem ferromagnetischen Resonanzanregungsschema (STXM-FMR), unter-sucht. Beide Messtechniken nutzen das gleiche FMR-Anregungsschema. Die direkte Abbildung von Spinwellen erfolgt mit höchster Zeit- und Raumauflösung und wird durch zeitaufgelöste mikromagnetische Simulationen untermauert. Messungen und mikromagnetische Simulationen zeigen, dass Spinwellen, die in einem begrenzten Py-Rechteck-Mikrostreifen angeregt werden, überraschenderweise sowohl bei Resonanz- als auch bei Off-Resonanz-Feldern unter gleichmäßiger Mikrowellenanregung einen nicht-stehenden Charakter aufweisen.

Ein nichtstehender Charakter von Spinwellen in komplexeren Py-Mikrostrukturen wird durch direkte Abbildung beobachtet, zusammen mit einem Hinweis auf die Möglichkeit, das Spinwellenverhalten durch Modifikationen des Probendesigns (Anordnung der rech-teckigen Mikrostreifen) zu verändern. Mikrostrukturen, die aus zwei identischen, recht-winkligen Py-Mikrostreifen senkrecht zueinander bestehen, werden mit einem ähnlichen Ansatz wie bei den Einzelstreifenproben untersucht. Mit Hilfe von mikromagnetis-chen Simulationen wird das Vorhandensein der Spin-Wellen-Moden zusammen mit den quasi-uniformen FMR-Moden der Py-Streifen berechnet und durch mikroresonator-basierte FMR-Messungen bestätigt. Die Spin-Wellen werden im realen Raum mittels STXM-FMR abgebildet, was einen nicht-stehenden Charakter der Spin-Wellen ähnlich wie bei der Einzelstreifenprobe zeigt. Zusätzlich wird durch mikromagnetische Simula-tionen gezeigt und durch STXM-FMR bestätigt, dass das Spinwellenverhalten durch die lokalen magnetischen Streufelder beeinflusst werden kann, die durch unterschiedliche gegenseitige Mikrostreifenpositionen gesteuert werden.

Aufgrund seiner elementaren Selektivität kann STXM-FMR auch zur direkten Ab-bildung des Spin-Pumpens in einer Ferromagnet-Nonferromagnet-Heterostruktur ver-wendet werden. STXM-FMR erlaubt es, die räumliche Ausdehnung der Wechselstrom-Spinpolarisation in einem Co-dotierten ZnO-Film (Co:ZnO) direkt zu untersuchen, die durch Spin-Pumping von einem benachbarten Py-Mikrostreifen erzeugt wird. Die rel-ativen Phasen der dynamischen Magnetisierungskomponente der beiden Bestandteile werden verglichen und es wird festgestellt, dass sie nahezu gegenphasig sind. Die Korrelation zwischen den Verteilungen der magnetischen Anregung im Py-Streifen und im Co:ZnO-Film zeigt, dass lateral keine Eins-zu-Eins-Korrelation besteht. Die beobachtete Verteilung ist recht komplex, aber die Integration über größere Bereiche zeigt, dass sich die Spinpolarisation im Nichtferromagneten lateral über den Bereich

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viii des ferromagnetischen Mikrostreifens hinaus erstreckt. Daher lassen sich die Beobach-tungen besser durch eine lokale Spin-Pump-Effizienz und eine laterale Ausbreitung der ac-Spin-Polarisation im Nicht-Ferromagneten ¨uber den Bereich von einigen Mikrome-tern erkl¨aren.

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List of Figures

2.1 Simplified classification of magnetic properties of magnetic materials . . 6

2.2 Rectangular microstrip schematic . . . 10

2.3 Internal magnetic field (y-component) within the rectangular strip in easy and hard orientations . . . 11

2.4 Magnetization precession around the direction of the effective magnetic field schematic . . . 12

2.5 The frequency dependence of the FMR linewidth of FeNi0.62Zn0.26Al0.71 and FeNi0.48Zn0.42Al0.76 . . . 14

2.6 Frequency dependence of the resonance field values and the linewidth of CoxZn1−xO/Py heterostructures, Al/Py and Py films . . . 15

3.1 Sample designs schematic . . . 20

3.2 SiN membrane substrate schematic . . . 20

3.3 Photolithography and EBL processes schematic . . . 22

3.4 Stripes microantenna preparation overview . . . 23

3.5 EVG 620 Mask Aligner . . . 24

3.6 Test Py microstrips prepared using optical lithography . . . 25

3.7 Planar microantenna and microresonator designs . . . 26

3.8 EBL set-up schematic . . . 27

3.10 Py microstrip produced using EBL . . . 27

3.9 Magnetron sputtering and PLD processes main principle . . . 28

3.11 EBPVD and resistive evaporation processes main principle . . . 30

3.12 An example of an FMR spectrum of the rectangular Py microstrip mea-sured in easy orientation at room temperature . . . 32

3.13 The XMCD effect illustrated for the L edge absorption in Fe . . . 33

3.14 STXM combined with XMCD schematic . . . 33

3.15 Correlation between a periodic signal and x-ray pulses in a storage ring of a synchrotron . . . 34

3.16 FMR experiment geometry schematic and an example of a STXM-FMR measurement of the Py microstrip. SEM image of Py T-strips . . 35

3.17 Sample designs used in simulations . . . 36

3.18 Simulated FMR spectrum of a Py microstrip with a schematics of the spin configuration forming a spin wave . . . 37

3.19 Extracting spin-wave profiles overview from micromagnetic simulations 38 3.20 SLAC-measurements data processing steps . . . 39

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List of Figures xii

3.21 BESSY-measurements data processing steps . . . 40 3.22 The STXM chemical contrast image of the Py strip . . . 41 3.23 Extracting amplitude and phase data from STXM-FMR measurements 42 3.24 Plotting amplitude and phase profiles overviews . . . 43 3.25 Combined and normalized amplitude/phase data of a STXM-FMR

mea-surements . . . 44 4.1 Simulated FMR spectra of the perfectly rectangular 1_{× 5 × 0.03 µm}3

Py microstrip in easy and hard orientations . . . 46 4.2 3D visualization of the spin waves with 5 main anti-nodes in easy and

hard orientations . . . 47 4.3 Simulated FMR spectrum of the perfectly rectangular Py strip in easy

orientation stacked with an overview of the spin-wave profiles along and across the strip . . . 48 4.4 Simulated FMR spectrum of the perfectly rectangular Py strip in hard

orientation stacked with an overview of the spin-wave profiles along and across the strip . . . 50 4.5 Measured FMR spectra plotted together with the initial simulations for

the single rectangular Py strip in easy and hard orientations . . . 51 4.6 Measured and simulated FMR spectra of the single rectangular Py strip

shown together with simulated spin-wave profiles overviews in easy and hard orientations . . . 53 4.7 Overviews of the simulated spin-wave profiles and combined and

normal-ized amplitude/phase data extracted from STXM-FMR measurements along and across the Py strip in easy and hard orientations, along and across the strip . . . 55 4.8 Simulated and STXM-FMR-measured time evolution of mz(t) over one

period for easy and hard orientations at several field values . . . 57 4.9 Detailed amplitude and phase analysis of the resonances at 87.8 mT in

the easy orientation and 103.6 mT in the hard orientation . . . 58 4.10 Measured and simulated amplitude and phase profiles along the middle

part of the Py strip for the quasi-uniform mode and n = 3 spin wave in easy orientation and n = 3 spin wave in hard orientation . . . 59 4.11 Simulated and measured with STXM-FMR transient behavior of the Py

microstrip . . . 62 5.1 T- and L-strips designs schematic . . . 66 5.2 Measured and simulated FMR spectra of the Py T- and L-strips with the

external field applied along the horizontal and vertical strip at fMW =

14.1 GHz . . . 67 5.3 Angular dependent FMR measurement of the T-strips at 14.1 GHz . . 68 5.4 Simulated FMR spectra of the T- and L-strips at fMW= 9.43 GHz . . . 69

5.5 Simulated FMR spectra of the Py T- and L-strips in comparison to the simulated spectra of the single Py strip (fMW= 9.43 GHz) . . . 71

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List of Figures xiii

5.6 STXM-FMR measurements of the vertical strip of the Py T-strips at 113 mT with corresponding micromagnetic simulations at 114 mT . . . 72 5.7 SLAC-measurements of the vertical strip of the T- and L-strips at

dif-ferent fields and corresponding micromagnetic simulations at 104 mT . 73 5.8 Simulated FMR spectra with overviews of the combined and

normal-ized amplitude/phase data extracted from BESSY-measurements and simulated spin-wave profiles along the vertical strip of the Py T- and L-strips . . . 75 5.9 BESSY-measurements and corresponding simulations of mz(t) across the

vertical strip of the T- and L-strips demonstrated over one oscillation period at several fields . . . 77 6.1 FMR spectrum of the 50% Co:ZnO/Py strip sample measured at 14.025

GHz . . . 81 6.2 XRD ω_{−2θ scan of a 50% Co:ZnO film grown on the SiN membrane.}

In-tegral magnetic characterization of 50% Co:ZnO films grown on sapphire as well as on a SiN membrane . . . 82 6.3 Conventional STXM measurement of the Py strip on top of the 60%

Co:ZnO and 50% Co:ZnO film at the Co L3 edge . . . 83

6.4 Dynamic magnetic contrast at six relative phases between the microwave excitation and x-ray pulse for the 50% Co:ZnO/Py heterostructure at 9.447 GHz and 96 mT recorded at the Ni as well as the Co L3-edges . . 85

6.5 Integrated dynamic magnetic contrast over two precession cycles recorded for the main FMR mode at 9.447 GHz and 96 mT recorded at the Ni L3

-edge for the region of the strip or the region outside the strip. Cor-responding integrated dynamic magnetic contrast at the Co L3-edge

recorded with σ– and σ+ light. The corresponding point-by-point anal-ysis of resulting local amplitude and phase derived at the Ni and Co L3-edges . . . 86

6.6 Integrated dynamic contrast for a nonuniform FMR excitation of the Py strip at fMW= 9.447 GHz and H = 106 mT recorded at the Ni L3-edge

and the corresponding local amplitude and phase. Integrated dynamic magnetic contrast recorded at the Co L3-edge . . . 88

B.1 Difference of the simulated FMR spectra when changing the frequency 123 B.2 Difference of the simulated FMR spectra when changing the saturation

magnetization . . . 123 B.3 Difference of the simulated FMR spectra when changing the damping

parameter . . . 123 B.4 Difference of the simulated FMR spectra when changing the thickness . 124 B.5 Difference of the simulated FMR spectra when changing the shape of

the strip . . . 124 B.6 Difference of the simulated FMR spectrum in easy orientation when

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D.1 Simulated and measured FMR spectra of the Py strip in easy orientation along with overviews of an amplitude and a phase profiles along and across the strip . . . 139 D.2 Simulated and measured FMR spectra of the Py strip in hard

orien-tation along with overviews of an amplitude and a phase profiles along and across the strip . . . 140

List of Tables

4.1 Quasi-uniform and spin-wave resonance field values of the single Py strip obtained using initial and adjusted simulations, FMR, and STXM-FMR measurements. n is the number of anti-nodes within the length of the strip. . . 51 4.2 The list of adjusted simulations parameters (frequency f , saturation

magnetization Ms, damping parameter α, strip thickness L and lateral

shape of the strip) and their initial values with the description of the effect that each change of the parameter causes on the resulting FMR spectrum. . . 52

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Acronyms and Abbreviations

2D Two dimensional

30% Co:ZnO Co doped ZnO (Co0.3Zn0.7O)

3D Three dimensional

AFM Atomic force microscope

BESSY-measurements The STXM-FMR measurements carried out at the MAXY-MUS endstation of the UE46-PGM2 undulator beam-line at the Helmholtz-Zentrum Berlin during the low-alpha mode of the BESSY II synchrotron ring Co:ZnO Co doped ZnO (CoxZn1−xO)

DFT Discrete Fourier transform E-beam Electron-beam

Easy orientation External magnetic field is aligned in plane along the easy axis of the strip (along the longer side)

EBL Electron beam lithography

EBPVD Electron-beam physical vapor deposition FC Field cooled

FH Field heated

FMR Ferromagnetic resonance FWHM Full-width at half maximum

Hard orientation External magnetic field is aligned in plane along the hard axis of the strip (along the shorter side)

HZDR Helmholtz-Zentrum Dresden-Rossendorf ISHE Inverse spin Hall effect

LLE Landau-Lifshitz equation

LLGl Landau-Lifshitz-Gilbert equation xv

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List of Tables xvi

MW Microwave

OOMMF Three-dimentional object-oriented micromagnetic frame-work PC Computer

PLD Pulsed laser deposition Py Permalloy (Ni80Fe20)

RF Radio frequency rpm Rotations per minute

sccm Standard cubic centimeters per minute SEM Scanning electron microscope

SLAC-measurements The STXM-FMR measurements carried out at the beam-line 13.1 at the SLAC National Accelerator Laboratory at the SSRL

SQUID Superconducting quantum interference device SSRL Stanford Synchrotron Radiation Lightsource STXM Scanning transmission X-ray microscopy

STXM-FMR STXM detected FMR with the use of XMCD as a contrast mechanism TR-STXM Time Resolved STXM

UHV Ultra high vacuum UV Ultraviolet

XMCD X-ray magnetic circular dichroism XRD X-ray diffraction

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1

Introduction

Nowadays magnonics is attracting an increasing attention, as it proves to be a very promising direction of research for processing information as computing devices de-creased drastically in size over the past decades [1–4]. Magnons or spin waves are to be one of the options to replace electrons in this regard [5–8]. A wide range of geo-metrical systems of materials have been investigated at this point, thin films [9–11], multilayer nanostructures [12], magnonic crystals [13–16], magnonic waveguides [17–

19] and confined microstructures [20–22].

In this thesis one of the research aspects is focused on understanding the dynamic magnetic properties of confined structures, as it is important for the development of nanoscale computational devices. It was observed experimentally that the spins near the edges of a confined microstructure often behave as if they are “pinned” and are not allowed to precess [19]. Reflections at the edges cause spin-wave resonances, whenever the distance between the edges equals an integer number of half wavelengths, in other words, quantization of the spin-wave modes occurs [3]. The spin-wave spectrum of an ellipsoidal magnetic element can be calculated analytically [23, 24]. However, in most of the cases the magnetic elements used in applications have a non-ellipsoidal shape. It has been shown that the non-ellipsoidal shape and quality of the edges of these elements drastically affect their dynamic magnetic properties [21, 22]. In most of the cases spin-waves are investigated using a non-uniform excitation of the structure [5, 7,

11, 13]. However, in devices of a micro- or nano-scale a uniform or close to uniform excitation field can be easier realized, e.g. placing an element in a close proximity of an antenna. In a rectangular microstrip the pinning effect can be exploited to excite spin waves with an odd number of half wavelengths within the length of the strip using uniform radio-frequency (rf)/microwave (MW) driving fields [3, 25]. The quantization conditions for the modes of the rectangular confined structure were described in detail in [20]. Due to the high inhomogeneity of the effective field inside the structure in the direction parallel to the external static magnetic field the quantization conditions for a k-vector aligned in the same direction are complicated [26]. The latter makes the analytical calculations for the spin-wave dispersion and consequent analysis very complex. The other approach that can be used for the spin-wave analysis for such structures is an experimental research in combination with micromagnetic simulations. The experimental investigation on small scales close to the sub-micron range requires

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2

very sensitive experimental techniques. Moreover, if one wants to obtain information about time and space resolved magnetization dynamics or look into a multilayered structure, the measuring techniques are required to be quite sophisticated. The pos-sibility to excite and visualize spin-waves in micron-sized structures was shown to be possible by techniques such as Brillouin light scattering [21, 27] or spatially resolved ferromagnetic resonance force microscopy [28]. Later time-resolved scanning transmis-sion X-ray microscopy (TR-STXM) [29–31] has been combined with a phase-locked ferromagnetic resonance (FMR) excitation scheme (STXM-FMR). This recently re-ported STXM-FMR technique enables direct, time-dependent imaging of the spatial distribution of the precessing magnetization across the sample during FMR excitation with elemental selectivity [32–35].

In this thesis spin waves in lithographically fabricated confined rectangular Ni80Fe20

(permalloy, Py) microstrips are investigated. Py is a widely used material and its magneto crystalline anisotropy can be neglected as the material is amorphous. In case of such microstructures the shape anisotropy is the predominant contribution to magnetic anisotropy and potentially can be exploited in order to modify spin-wave behavior. With the development of highly sensitive planar microresonators it became possible to measure the FMR of a single ferromagnetic microstrip including FMR lines corresponding to spin-wave excitations [34, 36–39]. The presence of spin waves in a single Py microstrip under uniform microwave excitation was evidenced earlier using microresonator-based FMR and supported by micromagnetic simulations [38]. Those findings were corroborated by detailed investigations of comparable spin-wave modes in a Co microstrip with similar dimensions [39]. In this thesis spin-wave excitations in a single Py microstrip under uniform MW driving field are studied in statics and dynam-ics by means of micromagnetic simulations, microresonator-/microantenna-based FMR measurements and direct imaging with STXM-FMR. The influence of shape modifi-cations on a spin-wave behavior is investigated, which includes microstructure design variations that allow to alter the spin-wave behavior within the microstrips. In partic-ular, the results on two perpendicular Py microstrips with varied mutual positions of the strips were published in [22].

In spintronics the generation and manipulation of pure spin currents is in the focus of research activities. Amongst the utilized fundamental effects is spin pumping where a precessing magnetization of a ferromagnet being at FMR transfers angular momentum to an adjacent nonferromagnetic layer [40]. The transfer of angular momentum into the nonferromagnetic layer can be described as a spin current. The pumped spin current has a dc and an ac component corresponding to the reduction in the projection of the magnetization at FMR and the dynamic high-frequency magnetization, respectively [41–43]. Usually, spin pumping is electrically detected via the inverse spin Hall effect (ISHE) inside the nonferromagnetic layer that makes conducting high-Z materials such as Pt advisable for easy detection [42, 44, 45]. However, for a few other materials like semiconducting Ge [46], conducting SrRuO3 [47] and ZnO [48] spin pumping could

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versatile approach is to detect the presence of spin pumping via the increased FMR linewidth [43,49,50]. It is nowadays consensus between experiment and theory that the flow of angular momentum from the ferromagnet into the nonferromagnet represents another Gilbert-like damping mechanism. Such spin pumping heterostructures allow different nonferromagnetic materials to be used without the restriction of the ISHE as the detection channel. However, the advantages of using nonconducting materials have been pointed out for the ferromagnet [50], as well as the nonferromagnet [43]. Insulat-ing nonferromagnets have the advantage that the increased magnetic dampInsulat-ing is less influenced by other mechanisms like eddy-current damping [43]. A major drawback in general is that most of the experimental methods used so far detect spin pumping only indirectly, no matter if they rely on the ISHE or the increased FMR linewidth. In addition, in most approaches only the dc component of the pumped spin polariza-tion inside the nonferromagnet is measured. However, the ac component, which was theoretically predicted to be rather large compared to the dc component [41], was also observed experimentally in an Yttrium-iron-garnet (YIG)/Pt heterostructure [51] as well as in Py/Pt heterostructures via the ISHE [42, 52].

As a further step of the research in this thesis, the FMR is excited in a Py microstrip in contact with an adjacent nonferromagnetic Zn0.5Co0.5O (50% Co:ZnO), which is

cho-sen to be insulating, i.e., inaccessible by the ISHE. With the FMR excited in the microstrip the lateral extent of the generated spin polarization is investigated utilizing STXM-FMR. This basic approach has already been shown to be feasible for electrical spin injection into a nonferromagnetic metal [53] and very recently to probe the ac component in Py/Cu heterostructures [54], which was evidenced before using time-resolved measurements without spatial resolution [55]. The time-resolved detection scheme based on the internal picosecond (ps) time structure of the synchrotron allows to sample dynamics up to the gigahertz regime, i.e., FMR frequencies [32]. Finally, STXM-FMR also allows for probing the magnetic properties with element selectiv-ity, since the contrast mechanism is based on the x-ray magnetic circular dichroism (XMCD) [56]. In view of this, the dynamic out-of-plane component of the precessing magnetization during FMR can be measured. Therefore, the magnetic response of the driving ferromagnet and the pumped spin polarization inside the nonferromagnetic material can be probed directly and independently. The results of this part of the research are published in [57].

This thesis is structured as follows:

Chapter 2

A general introduction to different types of magnetic materials is given, followed by the description of energy contributions that should be taken into account when analyzing ferromagnetic materials and a discussion of the influence of the shape anisotropy on magnetic properties of a rectangular microstructure. Furthermore, the basics of FMR are presented alongside a brief introduction of spin pumping. Finally, the quantization of the spin waves in rectangular confined structures is described.

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Chapter 3

Samples and microresonators’/microantennas’ preparation details are explained, in-cluding such methods as lithography, magnetron sputtering, pulsed laser deposition (PLD), electron beam physical vapor deposition (EBPVD) and resistive thermal evap-oration. Furthermore, microresonator-/microantenna-based FMR and STXM-FMR are introduced along with micromagnetic simulations. Additionally, the detailed ex-planation of the data analysis and visualization methods used for this thesis.

Chapter 4

Results of initial micromagnetic simulations are presented showing the range of spin waves that can be excited in a strip with dimensions of 1_{×5×0.03 µm}3_{when keeping the}

MW frequency constant and changing the external static magnetic field. Furthermore, microantenna-based FMR measurements are discussed in comparison to the initial simulations. Finally, results of the STXM-FMR measurements showing spin dynamics within the strip are compared with adjusted simulations.

Chapter 5

Results for the two perpendicular Py microstrips (T-strips and L-strips) are presented and discussed, including micromagnetic simulations and microresonator-based FMR. Further, T-strips, L-strips and a single strip are compared to each other. Finally, the STXM-FMR measurements showing spin dynamics within the vertical strip of the T-strips are compared to the L-T-strips. Part of the results discussed in this chapter are published in [22].

Chapter 6

Results for the 50% Co:ZnO/Py heterostructure are presented and discussed. First, results of the multifrequency FMR measurements are presented. Further, preliminary microresonator-based FMR measurements are shown, followed by the results of the x-ray diffraction (XRD) and superconducting quantum interference device (SQUID) magnetometry. Finally, the STXM-FMR measurements allow to detect the pumped ac spin polarization in the Co:ZnO layer within and outside of the Py microstrip region.

Chapter 7

A summary, conclusion of the obtained results are presented and an outlook for the further research is given.

Appendixes

Includes examples of Wolfram Mathematica and Python scripts used for the data anal-ysis; examples of OOMMF simulations configuration files and detailed plots for pa-rameters tuning for a single Py strip; and some additional STXM-FMR results not included in the main text.

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2

Theoretical Background

In this thesis, the dynamic magnetic properties of Ni80Fe20(permalloy, Py) microstrips

and heterostructures consisting of a Co doped ZnO (Co:ZnO) film and a Py microstrip were studied. In order to understand the spin dynamics in confined structures and het-erostructures a general introduction to different types of magnetic materials is given in this chapter. This is followed by the description of energy contributions that should be taken into account when analyzing ferromagnetic materials. Moreover, the influ-ence of the shape anisotropy on magnetic properties of a rectangular microstructure is discussed. Furthermore, the basics of ferromagnetic resonance (FMR) are presented alongside a brief introduction of the spin pumping. Finally, the quantization of the spin waves in rectangular confined structures is described.

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2.1. Ferromagnetism 6

2.1 Ferromagnetism

In a very generic approach all materials can be divided into two major groups depending on whether they have permanent magnetic moments or not. This simplified classifica-tion of the magnetic properties of the materials is represented by the block-scheme in Fig.2.1.

Fig. 2.1: Simplified classification of the magnetic properties of magnetic materials. Adapted from [25].

If a material does not possess permanent magnetic moments and magnetic moments get induced by application of an external magnetic field and are opposed to the field, the material belongs to the first group of diamagnetic materials. If a material does possess permanent magnetic moments, but the moments do not show a long-range order, the material is classified as paramagnetic. Materials with a spontaneous long-range order can be further divided in three subgroups: ferromagnetic, ferrimagnetic and

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antiferromagnetic, depending on the mutual orientation of the neighboring magnetic moments and their magnitudes. The scheme shown in Fig.2.1 is simplified, e.g. Pauli paramagnetism and Van Vleck paramagnetism are not included there, as those are not important for the presented work.

In ferromagnetic materials elementary magnetic moments exhibit spontaneous parallel alignment below the Curie temperature within respectively large volumes (compared to the inter-atomic dimensions) due to the exchange interaction. In the absence of the external magnetic field magnetization of the magnetic domains varies its orientation along the material volume in a way, that the stray field outside the sample is minimal. Above the Curie temperature thermal excitations exceed the exchange coupling and the magnetic order is lost when no external field is applied.

When considering a confined ferromagnetic microstructure, the following energy con-tributions should be taken into account:

E = EZeeman+ Edipole+ Eexch+ Eanis, (2.1)

where EZeeman is the Zeeman energy that strives to align magnetic moments parallel

to the external magnetic field, Edipole is the dipole-dipole interaction energy that aims

to reduce total magnetization and/or aligns it preferably along the longest dimension of a given specimen, Eexch is the exchange energy that favors all magnetic moments

to be aligned parallel to each other and Eanis is the magneto-crystalline anisotropy

that strives to align magnetic moments along preferable directions with respect to the crystalline structure [25].

The Zeeman energy is the change in energy of a magnetic moment ~M when it is put in the external magnetic field ~H [58]:

EZeeman =−µ0M~ · ~H , (2.2)

The energy depends on the angle between the magnetic moment and external magnetic field and is minimum, when those are parallel to each other.

The dipole-dipole interaction energy is originating from the interaction of magnetic dipoles of the body with the internal field created by the other dipoles of the material (demagnetizing field). For a body with a magnetization ~M (~r) and no external field applied the energy is [58]:

Edipole =− 1 2 Z V µ0H~d· ~M d3r− 1 6 Z V µ0M2d3r , (2.3)

where ~Hd is the demagnetizing field created by the body within itself (the same field

outside the material is called stray field). The second term tends to align all the moments in the same direction. This term can be neglected as it is much smaller

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compared to the exchange energy, thus (2.3) can be simplified to the form: Edipole=− 1 2 Z V µ0H~d· ~M d3r , (2.4)

if the integral is over the volume of a magnet, or Edipole=− 1 2 Z µ0Hd2d 3_{r ,} _(2.5)

if the integral is over all space and taking into account relation [58]: ~

B = µ0( ~H + ~M ) , (2.6)

where ~H = ~Hd in this case, and

Z ~

B_{· ~}Hdd3r = 0 , (2.7)

when no currents are present. As a result the magnetization of the body tends to form the configuration that is minimizing the dipole-dipole interaction energy (do-main structure). The dipole-dipole interaction energy is also sometimes referred to as demagnetizing energy [33, 59].

The exchange interaction is of quantum mechanical origin and indicates an interaction between neighboring spins. Using the Heisenberg model the total energy for the ith spin interacting with its neighbors can be written as [25]:

E_exchi =₋₂X

j

JijSˆi · ˆSj, (2.8)

where the sum is usually taken only over the nearest neighbors of i, Jij is an

ex-change constant between the ith and jth spin, and ˆSi(j) = ¯h₂σ = ˆˆ xσx+ ˆyσy+ ˆzσz are

spin operators with Pauli spin matrices σx,y,z [25]. The energy is minimum when the

neighboring spins are parallel (Jij > 0 → ferromagnetism) or antiparallel (Jij < 0 →

antiferromagnetism) to each other.

Magneto-crystalline anisotropy is the energy required to change the magnetization direction from the easy to the hard orientation with respect to the crystalline structure [60]. In the simplest case of uniaxial anisotropy when there is only one preferable direction (easy axis) the energy is:

Eanis= K1sin2θ , (2.9)

where K1 is the anisotropy constant and θ is the angle between the magnetization

direction and the easy axis. In case of iron, which has a cubic crystalline structure, there are three easy axes along the cube edges. In this case the magneto-crystalline

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anisotropy is four-fold and can be written as:

Eanis = K1 cos2θ1cos2θ2+ cos2θ2cos2θ3+ cos2θ3cos2θ1 +

+K2cos2θ1cos2θ2cos2θ3,

(2.10)

where θ1,2,3 are the angles between the magnetization and the cube edges [61]. For Py

microstructures that were used for this thesis the magneto crystalline anisotropy can be neglected as the material is amorphous. In case of such microstructures the shape anisotropy has much bigger contribution to the magnetic properties of the structure and should be taken in the main consideration.

2.1.1 Shape Anisotropy

Shape anisotropy is a consequence of a strong dependence of the dipole-dipole in-teraction energy on a shape of a magnetic specimen. The main reason being the demagnetizing field, which influences the magnetization process. A simple example of this relation is an ellipsoid. A uniformly magnetized ellipsoid has a homogeneous demagnetizing field ~Hd that can be written as [58]:

Hdi =−NijMj i, j = x, y, z , (2.11)

where N is the demagnetizing tensor, represented usually with a 3_{× 3 matrix. The} elements (Nx, Ny, Nz) of the matrix in a diagonal form are called demagnetizing factors

and have the following relation:

Nx+ Ny+ Nz= 1 , (2.12)

Demagnetizing factors can be used to obtain the internal field distribution of a speci-men. In case of the ellipsoid placed in the external static magnetic field ~H the internal field ~Hint components are:

Hinti = Hi− NiMi i = x, y, z , (2.13)

or in general form:

~

Hint = ~H + ~Hd. (2.14)

The demagnetizing field of a rectangular strip is inhomogeneous as well as its mag-netization. As a result the internal field within the structure is also inhomogeneous and can vary strongly from the center to the edges of the strip. Calculation of the demagnetizing and, thus, internal field is complicated for a rectangular shape [58, 62–

64]. Nevertheless, some approximations and simplifications can be done in order to demonstrate the character of the demagnetizing field distribution and its influence on the internal field.

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Fig. 2.2: Schematic representa-tion of the rectangular microstrip. Adapted from [62].

An analytical solution for a stray (demagne-tizing) field ~Hd distribution of a

rectangu-lar element is reported in [62]. In Fig.2.2

a schematic of the rectangular microstrip is shown with indication of the coordinate axes orientation, orientation of the external mag-netic field and dimensions of the strip. In the figure l and w are the lateral dimensions of the strip and L is its thickness. For the solu-tion published in [62] a constant homogeneous

magnetization parallel to the y-axis is assumed within the volume of the strip shown in Fig.2.3(a). The center of the coordinate system (0,0,0) is placed in the middle of the strip (indicated in blue color in the figure). As a result the solution reported in [62] gives the following expressions for the components of the demagnetizing field Hdi(i = x, y, z) at the point of space with coordinates (x, y, z) [62]:

Hdx(x, y, z) = M0 4π 2 X k,l,m=1 (₋₁₎k+m+l × ln z + (₋₁₎mzb+ q [x + (₋₁₎k_x b]2+ [y + (−1)lyb]2+ [z + (−1)mzb]2 , (2.15) Hdy(x, y, z) =− M0 4π 2 X k,l,m=1 (₋₁₎k+m+l(y + (−1) l_y b)(x + (−1)kxb) |y + (−1)l_y b| |x + (−1)kxb| × arctan    x + (₋₁₎k_x b [z + (−1)mzb] |y + (−1)l_y b| q [x + (₋₁₎k_x b]2+ [y + (−1)lyb]2+ [z + (−1)mzb]2    , (2.16) Hdz(x, y, z) = M0 4π 2 X k,l,m=1 (₋₁₎k+m+l × ln x + (₋₁₎kxb+ q [x + (₋₁₎k_x b] 2 + [y + (₋₁₎l_y b] 2 + [z + (₋₁₎m_z b] 2 , (2.17) where M0 is the saturation magnetization, xb = w/2, yb = l/2, and zb = L/2. This

solution is limited to the case of the uniform magnetization and its error increases with an increasing value of ∆M = Mr− Ms, where Mr and Ms are the remnant and

saturation magnetization, respectively.

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Math-2.1. Ferromagnetism 11

Fig. 2.3: Plot of the y-component of the internal magnetic field within the rectangular strip in (a) easy and (b) hard orientation. Adapted from [20].

ematica 12 script (see Appendix A.1) in order to calculate and plot the internal field distribution within the strip. The result is shown in Figs.2.3(a) and (b) as a 3D-plot. The dimensions of the strip are: (a) w = 1 µm, l = 5 µm and L = 30 nm and (b) w = 5 µm, l = 1 µm and L = 30 nm. The external field ~H of 100 kA/m is aligned along the y-axis. The x- and y-axes on the plot indicate the position of the strip and the z-axis indicates the value of the Hint,y along the plane (x, y, 0). It is visible on the

plots that the internal field is highly inhomogeneous from the center to the edges of the strip in the direction of the external field. This inhomogeneity affects the magnetic properties of the structure, in particular, it introduces strong shape anisotropy. The parallel orientation of the external field ~H to the length of the strip in Fig.2.3(a) will be referred to as “easy orientation” and the perpendicular orientation in Fig.2.3(b) as “hard orientation”.

2.1.2 Ferromagnetic Resonance

Ferromagnetic resonance (FMR) is a proven powerful tool to study the dynamics of spin systems within the ferro-, para- and ferrimagnetic materials [23,24,36–39,65–67]. When a static magnetic field ~H is applied at an angle to the magnetization ~M of a system, the latter starts to precess around the direction of the effective field ~Heff and

its motion can be described with the Landau–Lifshitz–Gilbert equation (LLG) [59,68]: d ~M dt =−γµ0 ~M × ~Heff + α Ms ~ M _× d ~M dt ! , (2.18)

where γ is the gyromagnetic ratio, µ0 is the vacuum permeability and α is the Gilbert

damping constant. The effective field ~Heff represents the sum of all torque-producing

fields, e.g. applied field ~H, demagnetizing field ~Hd, and anisotropy field ~Hanis:

~

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Fig. 2.4: Schematic of the magnetization preces-sion around the direction of the effective magnetic field. Adapted from [60].

The first term in Eq. (2.18) describes the precessing part of the magnetization movement and the second term (damping) causes ~M to align in the direction of

~

Heff over the time as shown in Fig.2.4. If the damping

is zero, the magnetization precesses around the direc-tion of the effective field with a constant angle.

FMR is excited by applying a small time-varying, e.g. radio-frequency (rf) or microwave (MW), magnetic field ~h(t) _{⊥ ~}H to the specimen. The resonant en-ergy absorption from ~h(t) occurs, when the frequency of ~h(t) equals the frequency of the magnetization pre-cession [23,61]. The calculation of the FMR frequency ωres for a thin film was suggested by C. Kittel in [69].

It included solving Eq. (2.19) with an assumption that ~

H is aligned along the z-axis and in-plane of the film, ~h(t) is parallel to x-axis and components of ~H are

(Hx,−4πMy, Hz):

ωres

γ 2

= BH , (2.20)

where B is the magnetic induction in the film. These calculations were followed by the solution for a general ellipsoid introduced also by C. Kittel in [23]. The geometry used for the solution defined principle axes of the ellipsoid being parallel to x-, y-, z-axes, included the demagnetizing factors Nx, Ny, Nzand set ~H parallel to z-axis and

~h(t) parallel to x-axis. In this case the effective field components inside the ellipsoid [internal field - see Eq. (2.13)] are:

Heff,x = h− NxMx, (2.21)

Heff,y =−NyMy, (2.22)

Heff,z= H − NyMy, (2.23)

As a result the following FMR condition is obtained [23]: ω_res

γ 2

= [H + (Ny− Nz)µ0M ][H + (Nx− Nz)µ0M ] , (2.24)

Further research has shown that when calculating the resonance condition one should also take into account crystalline anisotropy. In general the effective field should include all torque inducing fields [70]:

~

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which can complicate calculations of the FMR condition using Kittel’s approach [71]. Another approach was suggested using a free energy F derivation in spherical coordi-nates [72,73]: ωres γ 2 = 1 M2 " Fθθ Fφφ sin2θ + cos θ sin θFθ − Fθφ sin θ − cos θ sin θ Fφ sin θ 2# , (2.26)

where free energy is defined as a sum of Zeeman, dipole-dipole interaction and magneto-crystalline anisotropy energies.

The resonance condition defines the frequency ωresof a uniform mode when all magnetic

moments within the specimen precess in phase. When the FMR condition is fulfilled, the magnetization precesses with constant opening angle and can be divided into static and dynamic parts:

~

M = ~Mstatic+ ~m(t) . (2.27)

FMR measurements provide information on the resonant absorption of the applied MW (in case of MW driving field) allowing for measuring the resonant susceptibility

ˆ

χ change. Thus, using conventional FMR it is possible to probe the dynamic part of the precessing magnetization:

~

m = ˆχ~h . (2.28)

FMR Linewidth

The linewidth of an FMR spectrum ∆H is a sum of homogeneous ∆HGilb and

inho-mogeneous ∆H2mag+ ∆H0 contributions [74]:

∆H = ∆HGilb+ ∆H2mag+ ∆H0, (2.29) where ∆HGilb(ω) = 2 √ 3 α γMs ω γ (2.30) results from the Gilbert damping term in Eq. (2.27) originating from dissipation of the spin angular momentum to the lattice [75]. ∆HGilb(ω) gives a linear contribution in

the frequency dependence of the linewidth. The next term:

∆H2mag(ω) = Γ sin−1 s [ω2 _{+ (ω} 0/2)2]1/2− ω0/2 [ω2_{+ (ω} 0/2)2]1/2+ ω0/2 (2.31)

results from the two-magnon mechanism with ω0 = γ(2K2⊥ − 4πMs) and K2⊥ being

the uniaxial anisotropy constant. ∆H2mag does not vary linearly at lower frequencies

and saturates at high frequency (see Fig.2.5(a)). ∆H0 is the “zero-field linewidth”

that does not depend on frequency and gives a vertical shift of ∆H frequency depen-dency. Thereby, the frequency dependence of the linewidth can be used to separate its contributions [74,76, 77].

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Fig. 2.5: The frequency dependence of the FMR linewidth of (a) FeNi0.62Zn0.26Al0.71

and (b) FeNi0.48Zn0.42Al0.76 [77].

An example of the linear Gilbert damping and non-linear damping with significant contribution of the two-magnon scattering was reported in [77], where an in-depth analysis of Zn/Al-doped nickel ferrites (NiZAF) grown by reactive magnetron sputter-ing was performed. The material is interestsputter-ing for applications in magnetoelectric and acoustic spintronics due to being insulating and ferromagnetic at room temperature. The research in [77] was performed in our research group and showed additionally a possibility to achieve an additional low magnetic damping by altering the composi-tion of the material. In Fig.2.5(a) the frequency dependence of the FMR linewidth of FeNi0.62Zn0.26Al0.71film is shown. One can see a clear sign for a non-linear two-magnon

scattering contribution to the damping in addition to the intrinsic linear Gilbert damp-ing. The fit (red line) includes ∆HGilb and ∆H2mag. Additionally, an inhomogeneous

contribution ∆H0 = 7.8 mT is apparent from the linewidth dependence [77]. A

com-parative sample with increased Zn content and composition FeNi0.48Zn0.42Al0.76showed

a clear linear frequency dependence of the linewidth resulting in Gilbert damping with α = 6.8_{× 10}−3 and no two-magnon scattering or inhomogeneous contribution (see Fig.2.5(b)).

2.1.3 Spin Pumping

Spin pumping is a transfer of angular momentum from precessing magnetization of a ferromagnet being at resonance to an adjacent nonferromagnet through an interface. It results in the generation of spin current in the nonferromagnetic layer and the en-hancement of the magnetization damping in the ferromagnetic layer [40, 57, 75]. The pumped spin current has a dc and an ac component corresponding to the reduction of

~

Mstatic and ~m(t) [see Eq. (2.27)], respectively [41–43].

In FMR experiments spin pumping can be detected via increased linewidth of the ferromagnetic layer due to the enhanced damping constant α0 [40, 76]. The

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enhance-2.1. Ferromagnetism 15

Fig. 2.6: Frequency dependence of (a) the resonance field values with the example of the FMR spectrum of 50% Co:ZnO/Py at 6.58 GHz and its Lorentzian fit in the inset and (b) the linewidth with corresponding defined damping parameters in the inset. Adapted from [76].

ment of the constant depends on the spin-mixing conductance g↑↓, which describes the efficiency of the spin-current absorption of the nonferromagnet and depends on the interface quality between the two layers [40]:

α0 = g

↑↓_gµ B

4πMsV

, (2.32)

where g, Ms and V are the g-factor, saturation magnetization and the volume of the

ferromagnet, respectively. The equation shows that the effect depends on the inverse thickness of the ferromagnetic layer.

Previous research in our research group has shown that at room temperature an increase in the Gibert damping parameter is observed in multifrequency FMR measurements for 50 % Co:ZnO/Py and 60 % Co:ZnO/Py heterostructures and not for 30% Co:ZnO/Py [76]. In Fig.2.6(a) one can see that the resonance position of the heterostructures are the same as for the Py film. The linewidth frequency dependence in Fig.2.6(b) demon-strates a significant increase of the damping parameter for 50 % Co:ZnO/Py and 60 % Co:ZnO/Py, indicating spin pumping from Py into Co:ZnO [76]. The direct experi-mental evidence of the presence of a pumped spin polarization in the nonferromagnet is however lacking based on Fig.2.6(b) only and is also inaccessible for the detection via the ISHE, since Co:ZnO is highly insulating.

In this thesis the ac component of the pumped spin polarization directly inside the nonferromagnet is investigated with ultimate spatio-temporal resolution and elemental selectivity. This is achieved by using a time-resolved detection scheme in combination with a scanning transmission x-ray microscope (STXM-FMR, will be explained in detail in section 3.2.2) [32, 33]. In combination with a microwave excitation this STXM-FMR setup allows to excite the STXM-FMR of a ferromagnetic microstructure in contact with an adjacent nonferromagnetic insulator. This combination allows to utilize the

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2.2. Spin Waves in a Rectangular Microstrip 16

known lateral resolution of a few tens of nanometers of the STXM to investigate the lateral extent of the generated spin polarization. This basic approach has already been shown to be feasible for electrical spin injection into a nonferromagnetic metal [53] and very recently to also probe the ac component in Py/Cu heterostructures [54], which was evidenced before using time-resolved measurements without spatial resolution [55]. The time-resolved detection scheme based on the internal picosecond time structure of the synchrotron allows us to sample dynamics up to the gigahertz regime, i.e., FMR frequencies [32, 33]. Finally, STXM-FMR also allows for probing the magnetic properties with element selectivity, since the contrast mechanism is based on the x-ray magnetic circular dichroism (XMCD) [56]. In view of this, the dynamic out-of-plane component of the precessing magnetization during FMR can be measured. Therefore, the magnetic response of the driving ferromagnet and the pumped spin polarization inside the nonferromagnetic material can be probed directly and independently [57].

2.2 Spin Waves in a Rectangular Microstrip

Confined thin ferromagnetic microstructures show rich spectra of spin waves that can be excited by a uniform periodic magnetic field [78]. It was observed experimentally that the spins near the edges of a confined microstructure often behave as if they are “pinned” and are not allowed to precess [19]. Reflections at the edges cause spin-wave resonances, whenever the distance between the edges equals an integer number of the half wavelength, in other words quantization of the spin-wave modes occurs [3] (in rectangular elements quantization conditions get more complicated as described be-low in the section). The spin-wave spectrum of an ellipsoidal magnetic element can be calculated analytically [23, 24]. However, in most of the cases the magnetic ele-ments used in applications have a non-ellipsoidal shape and it has been shown that a rectangular shape and the quality of the edges of these elements drastically affect their dynamic properties [21, 22]. The reason for that is the strongly inhomogeneous magnetic field inside such structures when a uniform external static magnetic field is applied. As a result there are different effective field values within the rectangular microstrip corresponding to different spin-wave modes. The approximate dispersion equation for spin-wave eigenmodes in a thin (L/w_{1, L/l 1 - see Fig.}2.2) rectan-gular microstrip is [9,20, 26]:

ω_mn2 = (ω_Hmn+ λexωMk2mn)[ω mn

H + λexωMkmn2 + ωMFmn(kmnL)] , (2.33)

where ωmn = 2πf (kmn) is the excitation frequency, ~kmnis the in-plane wave vector with

its quantized values of the vector projections kmx and kny (k2mn = kmx2 + k2ny, m, n =

1, 2, 3, ...), ωM = γ4πMs with the saturation magnetization Ms, λex = Aex/2πMs2 is the

exchange constant in cm2, ωmn_H is proportional to the effective field value at the point (x, y):

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2.2. Spin Waves in a Rectangular Microstrip 17

where Nmn is the coordinate dependent demagnetizing factor. Fmn(kmnL) is a

quan-tized matrix element of the dipole-dipole interaction:

Fmn(kmnL) = 1 + P (kmnL)[1− P (kmnL)] ωM ωmn H + λexωMk2mn k2 mx k2 mn − P (kmnL) _k2 ny k2 mn , (2.35) where P (kmnL) = 1− 1_{− exp(−k}mnL) kmnL . (2.36)

The spatial distribution of the dynamic magnetization mmn(x, y) [see Eq. (2.27)] in

a rectangular microstrip shown in Fig.2.2 can be approximately represented using eigenfunctions ϕm(kmxx) of a longitudinally (~k⊥ ~M ) [79] and µn(knyy) of a transversely

(~k _{k ~}M ) [26] magnetized infinite long stripe [20]:

mmn(x, y) = ϕm(kmxx)µn(knyy) , (2.37)

where kmx and kny are the quantized values of the wave vector x and y components

respectively.

In the direction perpendicular to the external field spatial distribution ϕm(kmxx) is

given in [79]:

ϕm(kmxx) = Amcos(kmxx) (2.38)

for symmetric modes with an odd multiple of the half wavelength. Quantized values kmx in case of p = L/w 1 can approximately be expressed as:

kmx = mπ w 1₋ 2 d(p) , (2.39) where d(p) = 2π p[1 + 2 ln(1/p)] (2.40)

is the effective “pinning” parameter of magnetization at the lateral edges of the mi-crostrip.

Due to the high inhomogeneity of the internal field along the y-axis parallel to ~H (see Fig.2.3) the quantization condition for kny is more complicated compared to the x-axis

direction. An approximate evaluation of kny is given in [20]:

kny =

nπ ∆yn

, (2.41)

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in-2.2. Spin Waves in a Rectangular Microstrip 18

ternal field profile. Spin-wave modes in the direction parallel to ~H can be “exchange-dominated” and “dipole-“exchange-dominated”. Depending on the type of the spin-wave mode ∆yn differs: exchange-dominated modes localize near the strip edges perpendicular

to ~H and dipole-dominated localize near the strip center. The spatial distribution µn(knyy) also depends on the mode type and ∆yn, and in general can be described

using Eq. (2.38). In [20] it is demonstrated that the approximate analytical approach to the spatial distribution calculation based on the dispersion equation (2.33) is in a good quantitative agreement with micromagnetic simulation and experiment.

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3

Experimental Techniques and Data

Analysis

In this chapter preparation details of samples and microresonators/microantennas are explained. First, an overview of the sample designs, substrates used and preparation steps is given. Afterwards, the lithography part of the preparation process is described in detail including photolithography and electron beam lithography (EBL). Further-more, deposition methods such as magnetron sputtering, pulsed laser deposition (PLD), electron beam physical vapor deposition (EBPVD) and resistive thermal evaporation are explained. The main material for the microstructures investigated in this thesis was Py that was always capped with a 5 nm Al layer to prevent oxidation.

The measuring techniques such as microresonator-/microantenna-based ferromagnetic resonance (FMR) and combination of scanning transmission x-ray microscopy (STXM) with FMR using x-ray magnetic circular dichroism (XMCD) as a magnetic contrast mechanism (STXM-FMR) are described in detail concerning the work done for this thesis.

Along with the measurements the dynamic properties of the samples were simulated using Object Oriented Micromagnetic Framework (OOMMF) and MuMax3. The main parameters used for the simulations are listed. Finally, the data analysis and visual-ization methods are explained for further reference in the results part of the thesis.

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3.1. Sample Designs and Preparation 20

3.1 Sample Designs and Preparation

In the course of this thesis several sample designs were investigated (see Fig.3.1):

Fig. 3.1: Schematic of sample designs: (a) single strip, (b) T-strips, (c) L-strips, (d) Py strip on CoZnO.

(a) Single strip: a single Al-capped rectangular Py microstrip with lateral dimen-sions l = 5 µm, w = 1 µm and a thickness L = 30 nm;

(b) T-strips: two Al-capped rectangular Py microstrips each with lateral dimensions l = 5 µm, w = 1 µm and a thickness L = 30 nm. The strips are perpendicular to each other with a distance of 2 µm between them. The shorter edge of one of the strips is centred with respect to the longer edge of the second strip as shown in Fig.3.1(b);

(c) L-strips: two Al-capped rectangular Py microstrips each with lateral dimensions l = 5 µm, w = 1 µm and a thickness L = 30 nm. The strips are perpendicular to each other with a distance of 2 µm between them. The longer edge of one of the strips is aligned with the shorter edge of the second strip as shown in Fig.3.1(c); (d) Py strip on Co:ZnO: a single Al-capped Py microstrip with lateral dimensions l = 5 µm, w = 1 µm and a thickness L = 20 nm on top of the 50 nm thick Co doped ZnO (50% or 60% Co:ZnO) film.

Fig. 3.2: Schematic of a SiN membrane substrate. Two types of substrates were used for the sample

preparation depending on the planned measurements. For the STXM-FMR measurements a SiN membrane was used consisting of: (a) a layer of high resistive Si (>2000 Ω cm) frame 10.0_{×5.0 mm}2_{, 200 µm thick with}

a 0.25_{× 0.25 mm}2 _{window in the middle of the long}

side and with a 0.5 mm offset from the middle of the short side, and (b) 200 nm thick SiN membrane layer as shown in Fig.3.2. For the conventional measurements 5_{× 5 mm}2_{, 0.5 mm thick high resistive (>2000 Ω cm)}

Si (001) substrates with native oxide were used. The sample preparation was done in several steps (the de-tailed information including preparation parameters will be given in the sections 3.1.1 and 3.1.2):

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1. EBL + EBPVD (optional): magnetic markers. Markers, magnetic or non-magnetic, are additional microstructures placed in close proximity to a sample or its future position. They are used lateron in the lithography process for align-ment of the further microstructures such as Py microstrips and microresonator/ microantenna structures (will be explained in more detail in Sections 3.1.1 and

3.1.1). Non-magnetic markers were used for the samples measured with multifre-quency microantenna-based FMR. The structure of the markers was patterned using EBL and a 20 nm thick layer of Ti was deposited using EBPVD with sub-sequent lift-off process.

2. Magnetron sputtering (optional): 50 nm thick Co:ZnO film. The film was sput-tered using magnetron sputtering.

3. EBL + magnetron sputtering + PLD: a microstrip(s) structure and magnetic markers, if non-magnetic markers were skipped. The structure of the samples was patterned using EBL and a 30 nm thick layer of Py was deposited using magnetron sputtering. In order to protect Py from oxidation, the 5 nm thick capping layer of Al was deposited on top of Py using PLD. The e-beam resist was afterwards removed during the lift-off process.

4. Photolithography + EBPVD + resistive thermal evaporation: a microresonator/ microantenna structure was patterned with photolithography using a photomask, a nominally 5 nm thick adhesion layer of Ti was deposited using EBPVD. On top a 600 nm thick layer of Au was thermally evaporated and subsequently partially removed with a lift-off process.

The samples were produced using steps 1. to 3. using EBL and a consecutive step of photolithography for the planar microresonator/microantenna preparation around the sample structure. Each sample design was produced in a series of 2-4 pieces in case of possible sample damage during processing and also in order to control sample reproducibility. The sample material was grown using magnetron sputtering and PLD for capping. The resonator material was deposited using EBPVD for the Ti layer and resistive thermal evaporation for the Au layer. The quality of the samples was con-trolled using an optical microscope. In some cases an additional control was performed using scanning electron microscope (SEM) and atomic force microscopy (AFM). For the SEM imaging two systems were used, eLINE Plus EBL system described in more detail below in Section3.1.1 and Leo Supra 35 field emission SEM. The main principle is the same for both systems and is described in the Section 3.1.1. For imaging samples with Leo Supra 35 the electron energy of 5, 10 and 20 keV, aperture size of 30 µm, working distance of 4-9 mm and the inlens BSE-detector were used. For the imaging with AFM the VEECO Dimension 3100 was used in tapping mode. In this mode the cantilever is oscillating with (or near) its resonance frequency near the sample surface. The tracking of the sample surface is done by keeping either the

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amplitude or the phase of the oscillating cantilever constant [80]. This mode was chosen due to the relatively thick samples and microantennas/microresonators.

3.1.1 Photolithography and EBL

The general order of the photolithography and EBL with subsequent lift-off, carried out in this work, is shown in Fig.3.3. The main steps are as follows:

Fig. 3.3: Schematic overview of a photolithography and EBL processes. Adapted from [81].

(a) Spin Coating and soft baking: after pre-cleaning with acetone and iso-propanol the substrate is covered with a thin layer of an organic polymer (resist) sensitive to ultraviolet (UV) radiation (photo resist) or electron beam (e-beam resist). The resist is put on the substrate as a drop of solution and is spun at high speeds of 1500-8000 rotations per minute (rpm), which depends on the properties of the resist and its required thickness. After spin coating, the substrate is soft baked on a hot plate at around 100◦C for several minutes in order to remove possible solvents and stress from the resist and to improve adhesion.

Parame-ters set at this point: type of the resist, spin coating speed and time, soft baking temperature and time.

(b) Exposure: the resist is patterned by exposure to UV or e-beam. In case of a positive resist, used in this work, the exposed region weakens and becomes more soluble.

In case of photolithography the patterning is done using a photomask and UV radiation. The photomask is a transparent quartz plate with an image of the desired structure patterned on one side using a non-transparent material. In case of a positive resist the target pattern on the photomask is left transparent. Exposure is carried out by pressing the photomask against the photo resist and exposing it to a certain amount of UV radiation. Alignment of the substrate under the photomask is done using an optical microscope. As a reference point either substrate edges or previously patterned markers are used. Special trans-parent windows on the photomask are used for easier substrate alignment (see

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Fig.3.4(a)). Parameters set at this point: type of contact between substrate and

photomask (vacuum, hard or soft, depending on the pressure applied), time of exposure.

In case of EBL the patterning is done by steering a narrow focused beam of high-energy electrons (10-100 keV) across the e-beam resist on the substrate at regions, that need to be exposed. The process is often referred to as “writing a structure with EBL”. Alignment of the substrate is done using SEM and as a e-beam resist is sensitive to the electrons, edges of the substrate and/or markers are used for the alignment. Parameters set at this point: electron energy, aperture

size, dose or exposure time.

(c) Wet development: the resist is developed by a solvent that depends on the resist used in previous steps. The reaction is stopped with water or isopropanol. The development process removes the exposed part of the resist from the surface of the substrate producing a pattern that will serve as a mask for the deposited material. Parameters set at this point: development time (the rest depends on

the resist).

(d) Sputtering/deposition of a material: the desired material is sputtered or deposited on top of the resist mask and the noncovered substrate surface.

Pa-rameters set at this point: from the lithography perspective - the thickness, the deposition parameters that will be discussed in more detail in Section 3.1.2.

(e) Lift-off process: removal of the rest of the resist from the substrate surface. The part of the material that was on top of the resist is removed at this point. As a result only the part of the material that was deposited directly on the surface of the substrate is left. Parameters set at this point: solvent, solvent temperature,

duration length of soaking, usage of an ultrasonic bath.

Fig. 3.4: Stripes microantenna preparation overview: (a) an optical mask image, used for the resonator preparation and (b) schematic of the resonator on the substrate.

(40)

Photolithography

Photolithography with the use of photomasks is one of the most widely employed form of lithography in industry [82]. The main reason is a relatively fast process of a microstructure design transfer from a photomask to a photo resist. The limiting factor is resolution, i.e. the minimum feature size that can be exposed, also referred to as critical dimension. In photolithography the resolution depends on several factors such as radiation wavelength, ability of a photo resist to reconstruct the pattern, photo resist thickness, diffraction of the radiation on the edges of an image on a photomask, a gap between photomask and photo resist and its variation (tilt), the substrate reflective properties and surface quality, dirt on the photomask and/or resist, etc. The theoretical resolution R, that only takes diffraction effects into account, is given by [83]:

R = 3 2 r λs + z 2 , (3.1)

Fig. 3.5: Photo of the EVG 620 Mask Aligner.

where s is the gap between photomask and photoresist, λ is the wavelength of the ra-diation and z is the thickness of the pho-toresist. In contact mode, used for the sam-ple production in this work the photomask is pressed against the photoresist, which means that s = 0. considering the defects of the sub-strate, dirt and other factors, not included in the theoretical calculation, the approximate resolution of the photolithography using a vis-ible light for exposure is_{∼ 1 µm.}

In this thesis photolithography was carried out using an EVG 620 Mask aligner shown in Fig.3.5 and 150 mm quartz photo masks self-designed following previous research [35,

38,84] and produced by Toppan Photomasks, Inc. The main principle of the exposure process with the mask aligner was explained above when discussing Fig.3.3(b). The mask aligner is controlled by a desktop computer

EVG software. The alignment is done using a remotely controlled motorized stage while monitoring with built-in cameras. The set-up allows for different types of con-tact between photomask and photo resist, two of which were used for this thesis, soft contact for SiN-membrane substrates and hard contact for Si substrates.

In order to check if it is possible to fabricate microstrips using the available pho-tolithograpy facilities, a series of test samples was prepared. The rectangular struc-ture, patterned on the mask, with lateral dimensions l = 5 µm, w = 1 µm was used

Time Resolved Investigation of the Spin Dynamics in Laterally Confined Microstrips and Heterostructures / submitted by Santa Pile

Time Resolved

Investi-gation of the Spin

Dy-namics in Laterally

Con-fined

Microstrips

and

Heterostructures

Doctoral Thesis

Doktorin der Naturwissenschaften

Statutory Declaration

Abstract

Zusammenfassung

Contents

List of Figures

List of Tables

Acronyms and Abbreviations

1

Introduction

2

Theoretical Background

2.1

Ferromagnetism

2.1.1

Shape Anisotropy

2.1.2

Ferromagnetic Resonance

2.1.3

Spin Pumping

2.2

Spin Waves in a Rectangular Microstrip

3

Experimental Techniques and Data

Analysis

3.1

Sample Designs and Preparation

3.1.1

Photolithography and EBL